Quasi-objective coherent structure diagnostics from single trajectories

Abstract

We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures are quasi-objective: they approximate objective (i.e., observer-independent) coherence diagnostics in frames satisfying a certain condition. This condition requires the trajectory accelerations to dominate the angular acceleration induced by the spatial mean vorticity. We illustrate on examples how quasi-objective coherence diagnostics highlight elliptic and hyperbolic Lagrangian coherent structures even from very sparse trajectory data.

Objective momentum barriers in wall turbulence

“…Head & Bandyopadhyay 1981) also face objectivity as a minimal self-consistency requirement. Yet the Q-, λ 2 -, Δand λ ci -isosurfaces used for this purpose are not objective and hence their predictions for observed material tracer patterns, or momentum transport blocking, cannot be accurate (see Haller 2005Haller , 2021. While correlations may exist between measured scalar concentrations and the features of these non-objective diagnostics (e.g.…”

“…Westerweel et al 2009;Eisma, Westerweel & van de Water 2021), there can be no causal relationship. Several formal modifications of these vortex diagnostics have been proposed to make them objective, but only the approach of Liu, Gao & Liu (2019a); Liu et al (2019b) would be generally applicable, as found by Haller (2021). Yet, for lack of a direct connection to material mixing and transport, even correct objectivizations of the currently used Q-, λ 2 -, Δand λ ci -procedures for vortex identification would depend on their users.…”

“…Here, we use this recent theory of instantaneous active barriers to define and visualize both momentum trapping vortices and momentum blocking internal interfaces (MTBs) objectively based on their broadly envisioned role as minimizers of momentum transport. To adapt the active barrier field methods to large datasets, and numerically identify large invariant manifolds of the active barrier equations, we use recently developed single-trajectory-based objective coherent structure diagnostics, the trajectory rotation average (TRA) and trajectory stretching exponent (TSE), from Haller, Aksamit & Bartos (2021). Combining these theories, we develop a simple, systematic procedure that visualizes both MTBs and momentum-trapping vortices in general 3-D, wall-bounded turbulence.…”

Passive tracer advection in the equatorial Pacific region: statistics, correlations and a model of fractional Brownian motion

“…In most cases, it is possible to reconstruct invariant sets of a fractal nature in the phase space related to chaotic advection (see, e.g., Péntek et al, 1995;Cartwright et al, 1999;Tél et al, 2000;Speetjens et al, 2021). Recent important applications are connected to the exploration of Lagrangian coherent structures (Haller, 2015;Hadjighasem et al, 2017;Haller et al, 2018;Beron-Vera et al, 2018;Callies, 2021;Haller et al, 2021), mostly in the context of ocean flows.…”

Passive tracer advection in the equatorial Pacific region: statistics, correlations, and a model of fractional Brownian motion

“…Péntek et al, 1995;Cartwright et al, 1999;Tél et al, 2000;Speetjens et al, 2021). Recent important applications are connected to the exploration of Lagrangian coherent structures (Haller, 2015;Hadjighasem et al, 2017;Haller et al, 2018;Beron-Vera et al, 2018;Callies, 2021;Haller et al, 2021), mostly in the context of ocean flows.…”